Hi Berend
Thanks for your help. The model which l have mentioned shows that Pt is 
dependent on Ft, EXt, FAIt, My objecttive is not only to find the impact 
of these varibles on Pt but also to see the extent of effect of variables 
influencing  Ft, EXt, FAIt which are mentioned in respective equation 
2,3,4 on Pt. 
So, l m still not clear how creation of matrix A will help with my 
objective .
Regards,
Priya Saha


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From:   Berend Hasselman <bhh@xs4all.nl>
To:     Priya.Saha@zycus.com
Cc:     R help <r-help@r-project.org>
Date:   22-03-2012 15:50
Subject:        Re: [R] Simalteneous Equation Doubt in R




On 22-03-2012, at 09:15, Priya.Saha@zycus.com wrote:

> Hi List
> 
> l am interested in developing price model. I have found a research paper 

> related to price model of corn in US market where it has taken demand & 
> supply forces into consideration. Following are the equation:
> Supply equation:
> St= a0+a1Pt-1+a2Rt-1+a3St-1+a5D1+a6D2+a7D3+U1                -(1)
> Where   D1,D2,D3=Quarterly Dummy Variables(Since quarterly data are 
> considered)
> Here, Supply equation has 1 endogenous (St) & 6 exogenous variables  (P
> t-1,Rt-1,St-1,D1,D2,D3) 
> Demand Side: 
> Demand of corn is divided into 3 equations:
> Feed equation:
> Ft=b0+b1Pt+b2P(sm)t+b3Bt+b4COFt+b5Ht+a6D1+a7D2+a8D3+U2           -(2)
> here there are 2 endogenous variable(Ft, Pt) & 7 exogenous variables 
> (P(sm)t,Bt,COFt,D1,D2,D3) 
> Export equation:
> EXt= c0+c1Pt+c2EXt-1+c3Wt+c4DXt+c5GDPt+c6D1+c7D2+c8D3+U3         -(3)
> here there are 2 endogenous variable(EXt, Pt) & 7 exogenous variables 
(EX
> t-1,Wt,DXt,D1,D2,D3) 
> Food, Alcohol, Industry (FAI) Demand Equation:
> FAIt= d0+d1Pt+d2Etht+d3Popt+d4Tt+d5D1+d6D2+d7D3+U4      -(4)
> here there are 2 endogenous variable(FAIt, Pt) & 6 exogenous 
variable(Eth
> t,Popt,Tt,D1,D2,D3) 
> Price Equation: price of corn is determined by supply and demand 
> simultaneously, following is the reduced form equation: 
> Pt=ľ0+ľ1St+ľ2Ft+ľ3EXt+ľ4FAIt+ľ5Pt-1+ľ6D1+ľ7D2+ľ8D3+U5               -(5)
> here there are 5 endogenous variable(St, Ft,EXt, FAIt, Pt) & 4 exogenous 

> variable(Pt-1,D1,D2,D3)
> Now my question is :
> By applying 3SLS in the price equation, it will show the impact of 
> variables on Pt which are mentioned in equation (5).But if l want to 
find 
> impact of ETHt from equation (4) on Pt , l'll have to substitute 
equation 
> (1),(2),(3),(4) in price equation(5), which manually becomes very 
tedious, 
> is there any way this could be done directly in R?

Your system can be written compactly as

St  =                    + zS
Ft  = b1Pt               + zF
EXt = c1Pt               + zEX
FAIt= d1Pt               + zFAI
Pt  = ľ2Ft+ľ3EXt+ľ4FAIt  + zP

St is exogenous so can be ignored.
The system is linear and can be written as where the zXXX are the 
exogenous terms of the equation for XXX.

( Ft   )      ( 0   0  0 b1 )  ( Ft   )         ( zF   ) 
( EXt  ) = ( 0   0  0 c1 )  ( EXt  )      +  ( zEX  ) 
( FAIt )      ( 0   0  0 d1 )  ( FAIt )         ( zFAI ) 
( Pt   )      ( ľ2 ľ3 ľ4  0 )  ( Pt   )         ( zP   ) 

(Note: read the stacked ( and ) as a single large ( or ))
or

y = A %*% y + z

which can be written as

y = solve(diag(4)-A) %*% z

You only need to construct the matrix A.

Berend






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